The Göttingen School of Hilbert

Abstract

The fourth and final part of this book culminates in the the ground-breaking papers of Hermann Weyl on the representation of semisimple Lie groups (Chapter 12). For a full historical appreciation of Weyl’s work and the events leading up to it (Chapter 11), however, it is necessary to be mindful of the historical context in which Weyl developed as a mathematician. That context was provided by the school of mathematics that grew up around David Hubert at the University of Göttingen. Weyl was there from 1904 until 1913, first as a student, writing his doctoral dissertation under Hilbert’s supervision, and then as a lecturer (Privatdozent). Weyl himself has made it clear that Hilbert exerted a great influence upon him, and to make this point one can do no better than to quote the eloquent Weyl himself: “I came to Göttingen as a country lad of eighteen .… In the fullness of my innocence and ignorance I made bold to take the course Hilbert had announced for that term, on the notion of number and the quadrature of the circle. Most of it went straight over my head. But the doors of a new world swung open for me, and I had not sat long at Hilbert’s feet before the resolution formed itself in my young heart that I must by all means read and study whatever this man had written” [1944b: 132]. That Weyl was deeply affected by what he read is also clear. On the occasion of Hilbert’s seventieth birthday, he wrote of “the magic that his scientific personality exerts on the following generation,” and speaking for that generation, he added, “the mathematical way of thinking conveyed by our works, the special style of our mathematical thought, goes back to him more so than to any other living person” [1944a: 128].